What is the extreme f(x)=5x^3-3x^4 ?

The extreme f(x)=5x^3-3x^4 is Saddle(0,0),Maximum(5/4 , 625/256)

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extreme f(x)=5x^3-3x^4

extreme

Saddle (0, 0), Maximum (\frac{5}{4}, \frac{625}{256})

Solution steps

f^{'} (x) = 15 x^{2} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{5}{4},

Decreasing

: \frac{5}{4} < x < \infty

Plug

x = 0

into

5 x^{3} - 3 x^{4} : 0

Saddle (0, 0)

Plug

x = \frac{5}{4}

into

5 x^{3} - 3 x^{4} : \frac{625}{256}

Maximum (\frac{5}{4}, \frac{625}{256})

Saddle (0, 0), Maximum (\frac{5}{4}, \frac{625}{256})

What is the extreme f(x)=5x^3-3x^4 ?
The extreme f(x)=5x^3-3x^4 is Saddle(0,0),Maximum(5/4 , 625/256)